Artículo de Investigación. Revista Killkana Técnica. Vol. 1, No. 3, pp. 9-16, Septiembre-Diciembre, 2017. p-ISSN 2528-8024 / e-ISSN 2588-0888. Universidad Católica de Cuenca
Carrera de Ingeniería Electrica, Unidad Académica de Ingeniería, Industria y Construcción
Universidad Católica de Cuenca, Ecuador dicazaa@ucacue.edu.ec
This paper presents the mathematical model, the simulations performed before the construction of an 800W wind turbine for the rural areas of Ecuador. Subsequently, the project went to a laboratory research stage and using the MATLAB some simulations were carried out seeking the highest possible performance. The simulations were based on the characteristic parameters of the wind turbine, which should provide energy to rural households, outside the network of conventional electrical distribution. The power generation is possible at very low speeds because the rotor of an alternator was used for this case, permanent magnets were coupled and has a dynamic orientation system product of sensation of greater wind flow through a weather vane. At the end the wind turbine was submitted to functional tests in the town of Puntahacienda of the Quingeo Parish of the Canton of Cuenca-Ecuador.
Este artículo presenta el modelo matemático, las simulaciones realizadas antes de la construcción de una turbina eólica de 800 W para las áreas rurales de Ecuador. Posteriormente, el proyecto pasó a una etapa de investigación de laboratorio y con el MATLAB se llevaron a cabo algunas simulaciones buscando el mayor rendimiento posible. Las simulaciones se basaron en los parámetros característicos de la turbina eólica, que debería proporcionar energía a los hogares rurales, fuera de la red de distribución eléctrica convencional. La generación de energía es posible a velocidades muy bajas porque el rotor de un alternador se usó para este caso, los imanes permanentes se acoplaron y tiene un sistema de orientación dinámica producto del censado de mayor flujo de viento a través de una veleta. Al final, la turbina eólica se sometió a pruebas funcionales en la localidad de Puntahacienda, en la Parroquia de Quingeo, en el cantón de Cuenca-Ecuador.
I. INTRODUCTION
HE Renewable energy sources such as solar, hydro, wind, biomass and photovoltaic, among the main ones,
are being used increasingly by many countries in the world and particularly in Ecuador, there is a growing research and implementation of these generation systems, not only as a technical-economic alternative to the oil crisis, but as a
response to the negative effects that originate on man and nature [1].
The alternative energies are gaining place in the present society since nowadays the increment of the fossil fuels and environmental problems have returned the have the leading role to these energies to be clean and inexhaustible. Among these options is the wind with the placement of generators
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10 Daniel Icaza
wherever there is fairly constant wind. Its use is viable in areas where the electricity grid does not reach, such as farms and, in particular, rural houses. To mention examples in Ecuador such as the Villonaco de Loja Project and Baltra Island in Galapagos [2].
Today we are obliged to look for new alternatives of electric energy due to the increasing consumption of an en- ergy that has a constant increment on prices, which in some cases, are prohibitive for the most dispossessed classes, and with a demand that increases with extraordinary speed [1].
The renewable energies are for Ecuador a binding part of the National Plan for Good Living (PNBV) and within its objectives for the year 2021 is that less than 60% of installed capacity must be covered with renewable energy. Projects like the one developed in this article contribute to this objective and also to the integration of the rural areas
ω0 = Angular velocity produced by wind to wind vane.
k = Spring constant given in N/m.
V2 = Contact voltage drop.
Rg = Generator resistance (Alternator).
Vg = Generated electromotive force.
CONT = Controller selected.
Ei = Input voltage to the controller.
E0 = Output voltage of the controller.
ωg = Angular velocity produced in the generator.
ω1 = Angular speed of entrance to the blades.
Rf , Lf = Stator-related impedance.
V1 = Utility voltage max. 12V.
R1 = Stator input resistance.
N1 , N3 = Number of turns of gears driven.
N2 , N4 = Number of turns of conductive sprockets.
Ks = Sensor constant (wind vane).
that does not have access to the distribution lines [3].
Ecuador is on the path to progress in the development of projects involving renewable energies, and sources of energy supply that have not yet been widely exploited, especially in the rural areas of our country, where in many
ω0 =
k
m
10N/m
=
0.4kg
dif
= 5rad/s, (1)
cases energy is still used on the basis of gasoline or diesel
generators.
Vf (t) = Rf if + L
, (4)
dt
II. SIMPLIFIED MATHEMATICAL MODEL
ωO
m
Vf (s) = (Rf + sLf )If (s), (5)
Vg (t) = Kg if (t), (6) Vg (s) = Kg If (s), (7) Vg (t) = Rg ia + V2 (t) + Kc E0 (t), (8)
Vg (s) − V2 (s) = Rg Ia (s) + Kc E0 (s), (9) V1 (t) = R1 if (t), (10) V1 (s) = R1 if (s), (11) Tm (t) = TL (t) + T 1 (t), (12)
T 1 (t) =
N2 N4
N N
Te (s), (13)
1
TL (t) = Jeq
3
dωm + B ω , (14)
dt eq m
V2 TL (s) = [Beq + Jeq (s)]ωm (s), (15)
N2 N4
R1 Rf Rg Ei
Beq = Bm +
N1 N3
BL , (16)
+ CONT
Jeq = Jm +
N2 N4
JL . (17)
V1 If Vf Lf + E0
N1, N2, N3, N4
ωg, Tg, Bg, Jg
N1 N3
III. TRANSFER FUNCTION
Using the principles of block reduction to feedback systems related to an output C (s) and input R(s) [4], we have:
C (s)
=
R(s)
G(s)
1 + G(s)H (s)
. (18)
FIG. 1. Simplified mathematical model of the DIAWIND-A2 wind turbine.
Applying (18) to our system [5, 6, 7, 8], first between
V3 (s) and V2 (s), we have:
1 1 N2 N4
b
V3 (s) =
Rf + sLf Beq + sJeq
N1 N3
. (19)
E0 (s)
1
1 + Ks
1 N2 N4
b
where
Rf + sLf Beq + sJeq
N1 N3
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Modeling, simulation and construction of the DIAWIND-A2 . . . 11
V (s)
CONT
E (s)
d (t)
1
R sL
1
B sJ
1 3
t N N
V (s)
Vg (s)
f f
V (s)
eq eq 2 4
K s
g
FIG. 2. Block’s diagram of the DIAWIND-A2 wind turbine.
D(s)
V1 (s)
Organizing terms,CwOeNhTave:
1
14.4s 2 295.2s 145
V f (s)
Finally applying (18) between the output Vf (s) and the input V1 (s), we get the transfer function:
V3 (s) =Vg (s)
Kb N2 N4 .
E0 (s)
N1 N3 (Rf + sLf )(Beq + sJeq ) + Kb N2 N4 Ks
K g (20)
Vf (s) = Kb N2 N4 CONT
. (21)
V1 (s)
[N1 N3 (Rf + sLf )(Beq + sJeq ) + Kb N2 N4 Ks ]s + CONT Kb N2 N4 Kg
Evaluating with:
i =
N2 N4 =
N1 N3
10.10 1
= .
20.300 6
Starting from (23)
12
V1 (s) = s ,
Lf =0.2 H
Vf (s) = 3
CONT
2
12 . (25)
Rf = 4Ω
14.4s
+ 295.2s
+ 145s + CONT s
Ks = Kg = 1
Beq = 0.6 N·m/rad/s
D(s)= Possible disturbance that can be generated by
turning the wind vane.
Jeq = 1.2 Kg·m2
Vf (s) 1
3 2
Vf (s) = CONT .
D(s)
14.4s
+ 295.2s
+ 145s
V1 (s)
[60(4 + . 0.6 + 1.2s) + 1]s + CONT
Taking the transfer function (23) we must now determine
E (s)
d (t)
(22)
the appropriate controller so we perform the following
V (s)
nizing t o
1
analyzes.
1 1 3
V (s)
CONT
K We tested with different controllers and the one that
Vf (s) =
R sL
B sJ . (23) t N N
eq eq 2 4
Vg (s) s)
1 .V2 (s)
295.2s2 + 145s + CONT
manages to satisfy is a [P I ] for CONT=Kp + KI .
Evaluating (20)
V3 (s) = 1
K s
K. (24)
Vf (s)
V1 (s)
Kp + KI
= ,
5s3 + 202.5s2 + 101s + (Kp + KI )
E0 (s)
14.4s2 + 295.2s + 1 g
D(s)
Vf (t = ) = lim Vf (s)
s→0
= lim
Kp s + KI
V1 (s)
Vg (s)
CONT
1
14.4s 2 295.2s 145
V f (s)
s→0 5s4 + 202.5s3 + 101s2 + Kp s + KI
= KI = 1.
KI
K g
FIG. 3. Simplified block diagram.
The characteristic equation is:
5s4 + 202.5s3 + 101s2 + Kp s + KI = 0.
It satisfies the stability of the system since all the coeffi- cients of the equation are different from zero [4].
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12 Daniel Icaza
Therefore we select a [PI]
Vf (s) = Kp s + KI
, (26)
DIAWIND-A2 as an improved version but very close to another wind turbine built by the author, the D-ICAZA-A1. Figure 6 shows the general design of the DIAWIND-A2
V1 (s)
14.4s4 + 295.2s3 + 145s2 + Kp s + KI
wind turbine, which is in accordance with the parameters
with values Kp = 1 and KI = 0.5, the transfer function is finally evaluated:
Vf (s) = s + 0.5
presented in sections II to III of this article [9, 10, 11, 1].
What is explained here is just a summary of the most impor- a detailed analysis and xtension is not possible
V (s)
14.4s4 + 295.2s3 + 145s2 + s + 0.5 , (27)
ument. However, this
Geometric location of the roots according to the design of the DIAWIND−A2 wind turbine
60
n that is quite reliable ers who like to design
0.86
40
0.94
20
0.76
0.64
0.5
0.34
0.16
ble energy so that they is able to optimize the nergy production. Then ed way.
0.985
0 70 60 50
40 30
20 10
−20
−40
0.985
0.94
0.86
−60
0.76
0.64
0.5
0.34
0.16
−80 −60 −40 −20 0 20 40
Real Axis (seconds−1)
FIG. 4. Simulation of the LGR of the DIAWIND-A2 Wind Turbine.
As shown in Fig. 4 the poles are in the left plane with respect to the imaginary axis so the system is stable.
Starting from (25) before a step entry, we obtain the
Load
3.5
−3
x 10
Impulse Response
FIG. 6. Internal structure of the DIAWIND-A2 wind turbine.
3
2.5
2
1.5
1
0.5
0
0 100 200 300 400 500 600 700 800 900
Time (seconds)
V. CONSTRUCTION AND ASSEMBLY
The design of each of the main and complementary elements must guarantee the stability of the wind turbine as well as support the different efforts, proper to the in- teraction of the kinetic chain. On the other hand, it must also consider the deformations that its elements/parts can suffer because of external factors such as temperature and push-ups produced by the wind. In many cases, small variations can lead to welding between elements or frictions that threaten the normal functioning of the wind turbine. In this particular case we have taken into account the geometric and dimensional tolerance levels at the time of
FIG. 5. Response to impulse DIAWIND-A2 Wind Turbine.
Fig. 5 shows that the system stabilizes after 700 seconds.
IV. CASE STUDY
A. Description
After the study and analysis of stability, it was thought in a next stage that is the design of the wind turbine
construction of the wind turbine, which is why we must consider the surface of its elements, especially the input, secondary and vertical axes. These processes are carried out using by chip cutting, and using machine tools, such as the parallel lathe, the universal milling machine, the grinding machine, the slitter, etc. To get the pieces of the geometric configuration and surface finishes of good quality. Making a wind turbine with a vision requires of many resources such as time, money and machinery, as
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Modeling, simulation and construction of the DIAWIND-A2 . . . 13
well as patience to initially construct a prototype. Due to the extension of this article, it is not possible to provide very detailed information regarding the construction of the model. In the construction of the DIAWIND-A2 wind turbine, the multiplication system has been improved. This system helps amplify consequently to the alternator where the electric energy is generated in direct current. The details of the machining and construction of the most important parts are detailed below.
FIG. 9. Detail of the dynamic positioning system.
maximum wind current, the energy is generated, passed through a charge controller and then stored in 12v DC batteries [12, 2].
In Fig. 10, observed all their complements, such as tower elevation, batteries, weather vane, charge controller, etc.
FIG. 7. Surface finishing of flat parts.
In Fig. 7, surface finishing operations are performed on flat pieces where the roughness ranges are quite demanding. This consists of polishing the surfaces with a grinding stone located in the flat grinding machine.
FIG. 8. Tower and wind turbine to be assembled.
Fig. 8 shows the tower with the wind turbine mounted on the top. The tower will also serve as a support for the positioning system depending on the wind direction where the wind flow is best used.
In Fig. 9, the entire set of the sealed orientation system is observed. Here, the internal iron spheres allow the entire structure of the wind turbine to be oriented according to the maximum wind currents sensed by the wind vane. The orientation system can rotate maximum 180 degrees so you should take the decision in its implementation if we install it to windward or leeward.
Once the wind turbine is positioned according to the
FIG. 10. Overview of the DIAWIND-A2 wind turbine and the project author.
After its construction, functional tests were carried out in the town of Puntahacienda-Quingeo, in the Canton of Cuenca, as shown in Fig. 11 [7] and the results in Fig. 12. For this purpose we based both the formulas: The defined wind power conversion [10, 11, 1, 13] and the data mea- sured during the tests, as follows:
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14 Daniel Icaza
FIG. 11. DIAWIND-A2 wind turbine installed for performance testing in
Puntahacienda-Quingeo [7].
1600
1400
1200
1000
800
600
400
200
0
DIAWIND−A2 wind turbine
DIAWIND−A2 wind turbine Power curve
0 2 4 6 8 10 12 14 16
Wind Speed (m/s)
The power of the turbine is given by [13, 14];
1
FIG. 13. Experimental Stabilized Power-Velocity Curve for the
DIAWIND-A2 wind turbine.
P = Cp ρair A v3 ηaer , (28)
2
where P is the power produced by sweeping the blades per unit area, C p = Betz coefficient, ρair = Air density, A is the area swept by the blades of the wind turbine and v is the speed of the wind.
A = 7.06 m2
Cp = 0.5
ρair = 1.01 Kg·m−3
ηaer = 0.57
The simulated electrical power curve vs. the average
power curve of the generation measured in the field is then shown in Fig. 12 as a function of the above parameters.
Mathematical Model vs Experimental Data wind turbine DIAWIND−A2
1600
1400
1200
VI. CONCLUSIONS
The DIAWIND-A2 wind turbine is an alternative version to the D-ICAZA-A1 wind turbine built by the same author and has been transformed into a passion to experiment with projects like the one indicated.
The mathematical model used for the construction of the wind turbine was very efficient and therefore the final results were very positive at the time of performing field tests.
The implementation of a multiplication box with a higher transmission ratio, in our case its ratio 1/60 gives us interesting results such as the wind turbine at a speed of 1.8 m / s and starts to generate energy, however in the characteristic curve of power generation Power-speed the
1000
800
600
400
200
0
Mathematical Model
Experimental Data
0 2 4 6 8 10
Wind Speed (m/s)
wind turbine DIAWIND-A2 behaves with a pattern very similar to the wind turbine D-ICAZA- A1.
According to this new experience it is possible to make substantial improvements to the mathematical model as the design of the wind turbine with the inclusion of other vari- ables and input values The machinery for the construction of the DIAWIND-A2 wind turbine exists in our environ- ment, the workforce as well. We would lack investment and promotion.
As I can see despite being a rather small machine in
FIG. 12. Comparative curves between the theoretical mathematical model and the experimental curve of the DIAWIND-A2 wind turbine.
Fig. 13 shows that speeds between 1.8 m/s and 10.1m/s generate different power values in proportion, while from
10 m/s to 17 m/s the generated power is 800 W. There is a small peak between 10m/s and 13 m/s that exceeds the value of 800 W, we consider it as a transient power. It is also important to indicate that by protecting the elements that integrate the wind turbine when it exceeds the speed of 17 m/s will act a dynamic brake in kind of shoe to the secondary axis.
size it is possible to start a power generation with fairly small wind speeds around 1.8 m /s and opens up a fairly important option of installing these machines in various places in Ecuador.
The generation of energy we have available in direct current but we can transform it into alternating current through an inverter equipment.
The calibration of the multiplication box with the adja- cent elements must be considered since a level of friction and offset of the cogwheels can generate an imbalance of the system and therefore a wind turbine efficiency much lower than usual.
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Modeling, simulation and construction of the DIAWIND-A2 . . . 15
VII. RECOMMENDATIONS
It is recommended to the researchers that for the trans- port of the field wind turbine is done with the utmost care and especially the blades must maintain their balance, hitting their parts can cause a malfunction.
VIII. GRATITUDE
I am grateful to the Universidad Católica de Cuenca for giving me the opportunity to lead the electrical engineering career and to participate in research. On the other hand, I also thank the Politécnica Salesiana University for provid- ing me with the laboratories which at the time were of great support to carry out this and other similar investigations.
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Recibido: 13 de diciembre de 2017
Aceptado: 30 de diciembre de 2017
Daniel Orlando Icaza Alvarez: Electrical Engineering from the Universidad Politécnica Salesiana in 2005; Mas- ter in Telecommunications Management at the Universidad Politécnica Salesiana 2008; Currently he serves as the Ca- reer Director of Electrical Engineering at the Universidad Católica de Cuenca.
Revista Killkana Técnica. Vol. 1, No. 3, Septiembre-Diciembre, 2017